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Simplifying 49 = -0.3476x2 + 10.948x + -23.078 Reorder the terms: 49 = -23.078 + 10.948x + -0.3476x2 Solving 49 = -23.078 + 10.948x + -0.3476x2 Solving for variable 'x'. Combine like terms: 49 + 23.078 = 72.078 72.078 + -10.948x + 0.3476x2 = -23.078 + 10.948x + -0.3476x2 + 23.078 + -10.948x + 0.3476x2 Reorder the terms: 72.078 + -10.948x + 0.3476x2 = -23.078 + 23.078 + 10.948x + -10.948x + -0.3476x2 + 0.3476x2 Combine like terms: -23.078 + 23.078 = 0.000 72.078 + -10.948x + 0.3476x2 = 0.000 + 10.948x + -10.948x + -0.3476x2 + 0.3476x2 72.078 + -10.948x + 0.3476x2 = 10.948x + -10.948x + -0.3476x2 + 0.3476x2 Combine like terms: 10.948x + -10.948x = 0.000 72.078 + -10.948x + 0.3476x2 = 0.000 + -0.3476x2 + 0.3476x2 72.078 + -10.948x + 0.3476x2 = -0.3476x2 + 0.3476x2 Combine like terms: -0.3476x2 + 0.3476x2 = 0.0000 72.078 + -10.948x + 0.3476x2 = 0.0000 Begin completing the square. Divide all terms by 0.3476 the coefficient of the squared term: Divide each side by '0.3476'. 207.3590334 + -31.49597238x + x2 = 0 Move the constant term to the right: Add '-207.3590334' to each side of the equation. 207.3590334 + -31.49597238x + -207.3590334 + x2 = 0 + -207.3590334 Reorder the terms: 207.3590334 + -207.3590334 + -31.49597238x + x2 = 0 + -207.3590334 Combine like terms: 207.3590334 + -207.3590334 = 0.0000000 0.0000000 + -31.49597238x + x2 = 0 + -207.3590334 -31.49597238x + x2 = 0 + -207.3590334 Combine like terms: 0 + -207.3590334 = -207.3590334 -31.49597238x + x2 = -207.3590334 The x term is -31.49597238x. Take half its coefficient (-15.74798619). Square it (247.9990690) and add it to both sides. Add '247.9990690' to each side of the equation. -31.49597238x + 247.9990690 + x2 = -207.3590334 + 247.9990690 Reorder the terms: 247.9990690 + -31.49597238x + x2 = -207.3590334 + 247.9990690 Combine like terms: -207.3590334 + 247.9990690 = 40.6400356 247.9990690 + -31.49597238x + x2 = 40.6400356 Factor a perfect square on the left side: (x + -15.74798619)(x + -15.74798619) = 40.6400356 Calculate the square root of the right side: 6.374953772 Break this problem into two subproblems by setting (x + -15.74798619) equal to 6.374953772 and -6.374953772.Subproblem 1
x + -15.74798619 = 6.374953772 Simplifying x + -15.74798619 = 6.374953772 Reorder the terms: -15.74798619 + x = 6.374953772 Solving -15.74798619 + x = 6.374953772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.74798619' to each side of the equation. -15.74798619 + 15.74798619 + x = 6.374953772 + 15.74798619 Combine like terms: -15.74798619 + 15.74798619 = 0.00000000 0.00000000 + x = 6.374953772 + 15.74798619 x = 6.374953772 + 15.74798619 Combine like terms: 6.374953772 + 15.74798619 = 22.122939962 x = 22.122939962 Simplifying x = 22.122939962Subproblem 2
x + -15.74798619 = -6.374953772 Simplifying x + -15.74798619 = -6.374953772 Reorder the terms: -15.74798619 + x = -6.374953772 Solving -15.74798619 + x = -6.374953772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.74798619' to each side of the equation. -15.74798619 + 15.74798619 + x = -6.374953772 + 15.74798619 Combine like terms: -15.74798619 + 15.74798619 = 0.00000000 0.00000000 + x = -6.374953772 + 15.74798619 x = -6.374953772 + 15.74798619 Combine like terms: -6.374953772 + 15.74798619 = 9.373032418 x = 9.373032418 Simplifying x = 9.373032418Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.122939962, 9.373032418}
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